Fuglede conjecture holds for convex planar domains

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Let $Ω$ be a compact convex domain in the plane. We prove that $L^2(Ω)$ has an orthogonal basis of exponentials if and only if $Ω$ tiles the plane by translation.

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Classical Analysis and ODEs

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http://salesiana.dossiersoluciones.com/handle/123456789/61260

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0104087
 http://arxiv.org/abs/math/0104087

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arXiv